Calculus Examples

$x + \frac{6}{x}$

Step 1

Write $x + \frac{6}{x}$ as an equation.

$y = x + \frac{6}{x}$

Step 2

Find the x-intercepts.

Tap for more steps...

Step 2.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = x + \frac{6}{x}$

Step 2.2

Solve the equation.

Tap for more steps...

Step 2.2.1

Rewrite the equation as $x + \frac{6}{x} = 0$ .

$x + \frac{6}{x} = 0$

Step 2.2.2

Find the LCD of the terms in the equation.

Tap for more steps...

Step 2.2.2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$1, x, 1$

Step 2.2.2.2

The LCM of one and any expression is the expression.

$x$

Step 2.2.3

Multiply each term in $x + \frac{6}{x} = 0$ by $x$ to eliminate the fractions.

Tap for more steps...

Step 2.2.3.1

Multiply each term in $x + \frac{6}{x} = 0$ by $x$ .

$x \cdot x + \frac{6}{x} x = 0 x$

Step 2.2.3.2

Simplify the left side.

Tap for more steps...

Step 2.2.3.2.1

Simplify each term.

Tap for more steps...

Step 2.2.3.2.1.1

Multiply $x$ by $x$ .

$x^{2} + \frac{6}{x} x = 0 x$

Step 2.2.3.2.1.2

Cancel the common factor of $x$ .

Tap for more steps...

Step 2.2.3.2.1.2.1

Cancel the common factor.

$x^{2} + \frac{6}{x} x = 0 x$

Step 2.2.3.2.1.2.2

Rewrite the expression.

$x^{2} + 6 = 0 x$

Step 2.2.3.3

Simplify the right side.

Tap for more steps...

Step 2.2.3.3.1

Multiply $0$ by $x$ .

$x^{2} + 6 = 0$

Step 2.2.4

Solve the equation.

Tap for more steps...

Step 2.2.4.1

Subtract $6$ from both sides of the equation.

$x^{2} = - 6$

Step 2.2.4.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{- 6}$

Step 2.2.4.3

Simplify $\pm \sqrt{- 6}$ .

Tap for more steps...

Step 2.2.4.3.1

Rewrite $- 6$ as $- 1 (6)$ .

$x = \pm \sqrt{- 1 (6)}$

Step 2.2.4.3.2

Rewrite $\sqrt{- 1 (6)}$ as $\sqrt{- 1} \cdot \sqrt{6}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{6}$

Step 2.2.4.3.3

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i \sqrt{6}$

Step 2.2.4.4

The complete solution is the result of both the positive and negative portions of the solution.

Tap for more steps...

Step 2.2.4.4.1

First, use the positive value of the $\pm$ to find the first solution.

$x = i \sqrt{6}$

Step 2.2.4.4.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - i \sqrt{6}$

Step 2.2.4.4.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = i \sqrt{6}, - i \sqrt{6}$

Step 2.3

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

x-intercept(s): $None$

Step 3

Find the y-intercepts.

Tap for more steps...

Step 3.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = (0) + \frac{6}{0}$

Step 3.2

The equation has an undefined fraction.

Undefined

Step 3.3

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

y-intercept(s): $None$

Step 4

List the intersections.

x-intercept(s): $None$

y-intercept(s): $None$

Step 5